204A-slides02b

204A-slides02b - (2b)-P.1 Applications of Growth Theory I:...

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Unformatted text preview: (2b)-P.1 Applications of Growth Theory I: Growth Accounting Objective: Use empirical data on output, capital stocks, and labor supply, to interpret history (accounting), to compare across countries, or to make projections. Data sets: observations (Y t , K t , L t ) at discrete dates t. - Productivity index A is not directly observable must be inferred. - Though capital and labor shares vary, commonly assume Cobb-Douglas: k ( k ) . - Common labels: Y/L = labor productivity vs. A = total/multi factor productivity Growth accounting with Cobb-Douglas production: - Write Y = K ( AL ) 1 = R K L 1 with R = A 1 = the Solow Residual => ln Y = ln K + (1 )ln L + ln R with ln R = (1 )ln A- Take time-differences to approximate growth [ math: d ln( x )/ dt = 1 x dx dt ln( x ) ] => ln Y = ln K + (1 ) ln L + ln R- General notation for growth over an interval: g x = 1 t 1 t [ln( x ( t 1 ) ln( x ( t )] => g Y = g K + (1 ) g L + g R (2b)-P.2 Decomposing Growth Rates Key equations: g Y = g K + (1 ) g L + g R = g K + (1 ) g L + (1 ) g A From the data: compute ( g Y , g K , g L ) for various time periods; estimate . - Use Cobb-Douglas to infer g R = g Y g K (1 ) g L or R = Y ( K L 1 )- Use R = A 1 to infer TFP: g A = g R /(1 ) or A = R 1/(1 ) Growth accounting for per-capita variables [Math: Growth of ratio = difference of rates]- Income: g Y / L = g Y g L = g K g L + g R = g K / L + g R- Growth in K/L called capital deepening . Conclude: Growth of per-capita income = Capital deepening and productivity growth.- Growth accounting means decomposition of growth rates into components. - Sometimes decompose further: multiple types of capital and labor, each weighted by its (2b)-P.2 Decomposing Growth Rates Key equations: g Y = g K + (1 ) g L + g R = g K + (1 ) g L + (1 ) g A From the data: compute ( g Y , g K , g L ) for various time periods; estimate . - Use Cobb-Douglas to infer g R = g Y g K (1 ) g L or R = Y ( K L 1 )- Use R = A 1 to infer TFP: g A = g R /(1 ) or A = R 1/(1 ) Growth accounting for per-capita variables [Math: Growth of ratio = difference of rates]- Income: g Y / L = g Y g L = g K g L + g R = g K / L + g R- Growth in K/L called capital deepening . Conclude: ....
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This note was uploaded on 12/26/2011 for the course ECON 240a taught by Professor Staff during the Fall '08 term at UCSB.

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204A-slides02b - (2b)-P.1 Applications of Growth Theory I:...

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